Expressing Vectors in x-y Coordinates & Calculating Magnitude & Direction

In summary, x-y coordinates are used to represent the location of a point in a two-dimensional coordinate system. To express a vector in x-y coordinates, its horizontal and vertical components must be determined. The magnitude of a vector is its length, which can be calculated using the Pythagorean theorem. The direction of a vector is the angle it makes with the positive x-axis and can be found using trigonometric functions.
  • #1
kjland
2
0
I'm sure this is a simple concept but i just can't wrap my brain around it, the question is:

a) Express the following vectors in terms of x-y coordinates:

i)Vector V with direction π/6 and magnitude 4√3.

ii) Vector W with direction 5π/4 and magnitude 4√2.

b) Express the vector v + w in terms of magnitude and direction.Thank you!
 
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  • #2
Here's a start:

a) i) $x=4\sqrt3\cdot\cos\left(\dfrac{\pi}{6}\right)$

Can you find $y$?
 

1. What are x-y coordinates?

X-y coordinates are a way of representing the location of a point in a two-dimensional coordinate system. The x-coordinate represents the horizontal position of the point, while the y-coordinate represents the vertical position.

2. How do you express a vector in x-y coordinates?

To express a vector in x-y coordinates, you need to determine the horizontal and vertical components of the vector. The horizontal component is the length of the vector projected onto the x-axis, and the vertical component is the length projected onto the y-axis. These components can then be written as a combination of the unit vectors i (in the x-direction) and j (in the y-direction), such as 3i + 2j.

3. What is the magnitude of a vector?

The magnitude of a vector is the length of the vector, which is calculated using the Pythagorean theorem. It is a measure of the vector's size or strength and is always a positive value.

4. How do you calculate the magnitude of a vector?

To calculate the magnitude of a vector, you need to find the square root of the sum of the squares of its horizontal and vertical components. This can be represented mathematically as √(x² + y²), where x and y are the horizontal and vertical components, respectively.

5. What is the direction of a vector?

The direction of a vector is the angle that the vector makes with the positive x-axis in a counterclockwise direction. It is typically measured in degrees or radians and can be calculated using trigonometric functions such as tangent.

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